F. R. Klinkhamer, C. Rahmede
A nonsingular localized static classical solution is constructed for standard Einstein gravity coupled to an SO(3)\times SO(3) chiral model of scalars [Skyrme model]. The construction proceeds in three steps. First, an Ansatz is presented for a solution with nontrivial topology of the spacetime manifold. Second, an exact vacuum solution of the reduced field equations is obtained. Third, matter fields are included and a particular numerical solution is found. This numerical solution has a negative effective mass, meaning that the gravitational force on a distant point mass is repulsive. Most likely, the origin of the negative effective mass traces back to the "surgery" needed to create the "defect" from Minkowski spacetime, but this process involves topology change and lies outside the realm of classical Einstein gravity.
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http://arxiv.org/abs/1303.7219
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